electrical power grid network optimisation by...

Electrical Power Grid Network Optimisation by Evolutionary Computing

John M. Oliver1, Timoleon Kipouros1 and A. Mark Savill1 1 Cranfield University, Cranfield, U.K.

[email protected]

Abstract A major factor in the consideration of an electrical power network of the scale of a national grid is the calculation of power flow and in part icular, optimal power flow. Th is paper considers such a network, in which d istributed generation is used, and examines how the network can be optimized, in terms of transmission line capacity, in order to obtain optimal or at least high -performing configurations, using multi-objective optimisation by evolutionary computing methods. Keywords: Multi-objective, Optimisation, Evolutionary Computing, Electrical Power, Grid

1 Introduction This work exp lores a possible method of addressing the configuration of large-scale electrical

power networks, such as a national grid, using an approach based on evolutionary computing, which has been used previously in complex systems research such as emergent computation (Mitchell, 1999) and dynamics of complex networks (Aguilar-Hidalgo et al., 2012), and also direct ly in OPF research (Pandya and Joshi, 2008). As described by Allen et al., (Allen et al., 2010), consideration of systems exhibit ing complexity entails the construction of synergies between the studies of systems and their structures, and the ideas of neo-Darwinian evolutionary processes.

The essential problem in the architecture o f national grid networks is that of power flow and optimal power flow (OPF) calculations of alternating current (AC) power, and these calculations are at the centre of Independent System Operator (ISO) power markets (Cain et al., 2013) in which AC OPF is solved over a number of different orders of magnitude of timescales, from minutes via hours, to annually and mult i-year horizons, where the latter is for planning and investment while the former are for ensuring demand is met and for spot market pricing. The ISO produces and acquires load forecasts, receives offers of power from generating companies acting within a competit ive auction market, and produces generation schedules consisting of required power units and a price, to meet demand within the constraints of the grid and generators.

Procedia Computer Science

Volume 29, 2014, Pages 1948–1958

ICCS 2014. 14th International Conference on Computational Science

1948 Selection and peer-review under responsibility of the Scientific Programme Committee of ICCS 2014c© The Authors. Published by Elsevier B.V.

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Electrical power networks can be improved both technically and economically through the inclusion of distributed generation (DG) which may include renewable energy sources. DG units are lower output generators that provide incremental capacity at specific geographical locations, th us enhancing voltage support and improving network reliability while also acting economically as a hedge against a high price of centrally produced power, through locational marg inal pricing (LMP) . The operation of grids by ISOs as unbundled auction wholesale spot power markets that support real-time pricing provides a further incentive to roll-out DG, thus arises the need to define the type, number and location of extra DG units (Gautam and Mithulananthan, 2007).

The work presented here addresses the composition of a DG AC electrical power network based upon the IEEE 30 Bus Test Case which represents a portion of the American Electric Power System (in the Midwestern US) in December 1961, and which was downloaded from (Christie, 1993). Th is network, as shown in Figure 1, is amended to have six central fixed large-scale open cycle gas turbine (OCGT) electrical power stations, and twenty four variable distributed generators, powered either by renewable energy sources, being solar photovoltaic (PV) or micro-wind turbine, or by micro gas turbine. In part icular, this work uses historical data of weather (in the form of actual solar PV and wind power generation), central power generation, and electrical energy demands, from Australia of 2010, thus providing a realistic simulation environment for both demand and renewable generation.

This work continues the investigation of optimising power networks by Oliver et al. (Oliver et al., Expected Ju ly 2014), by looking at the power capacity of t ransmission lines, as well as considering the number and types of DG unit used in the network. In this way, the network connections undergo an optimising process, as well as the nodes (the buses) comprising the network. The aims are then to determine the composition of the power network in terms of the type, number and location of the non-central DG units, allowing transmission line power capacity to become further variables within the optimisation, with the goal of finding the smallest capital cost in meeting the demand for power, while keeping over- and under-production of power as low as possible, and of min imizing the average spot price and CO2 emissions.

2 Background The Plexos tool (Energy Exemplar Pty Ltd, 2013) is incorporated to provide both OPF and

financial market simulations, in particular providing unit commitment (which generators should be used, bearing in mind their operating characteristics such as ramp-up time as well as power output and running costs), economic dispatch (which generators to use to meet demand from a cost viewpoint), transmission analyses (losses, congestion), and spot market operation. It also provides estimations of CO2 emissions. The volume of lost load (VoLL) is the threshold price above which loads prefer to switch off, while the dump energy price is that below which generators prefer to switch off, and these along with market auctions also contribute to the ratio of power generated to power consumed. Transmission losses are also taken into account within Plexos through sequential linear programming.

Plexos is integrated with a multi-objective optimizing evolutionary algorithm (MOOEA) (Oliver et al., 2013), thus establishing an optimization feedback loop, since Plexos gives optimal unit commitment for a g iven set of DG units, while the MOOEA is used to deter-mine the optimal set of generators for the given demand profile and weather pattern. A MOOEA is used as they have a history of tackling non-linear (Nicolis, 1995) mult i-objective and multi-dimensional optimizat ion problems successfully, and since OPF for AC power is a non-linear problem while power markets require multi-part non-linear pricing. In the model used here, there are seventy two parameters that constitute the design vector applicable to each candidate solution, represented as one individual in the MOOEA, thus the problem is both non-linear and multi-d imensional. The simulation has a horizon of

Power Grid Network Optimisation by Evolutionary Computing J. Oliver, T. Kipouros and M. Savill

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one calendar year, represented as 365 steps of 1 day increments with a resolution to 30 minutes, from 01-Jan-2010.

A MOOEA (Deb, 2001) is generally a heuristic, stochastic means of searching very large non-linear decision or objective spaces in order to attempt to obtain (near) optimal or high-performing solutions (Jones et al., 2002) for problems upon which classical optimization methods do not perform well. EAs are characterized by populations of potential solutions that converge towards local or global optima through evolution by algorithmic selection as inspired by neo -Darwinian (Coello Coello, 2006) evolutionary processes. An init ial population of random solutions is created and through the evaluation of their fitnesses for selection for reproduction, and by the introduction of variation through mutation and recombination (crossover), the solutions are able to evolve towards the optima. MOO produces a set of trade-off solution points (Fonseca and Fleming, 1995) since all objectives are optimised simultaneously, giving rise to individuals that cannot be improved upon in one OF dimension without being degraded in another. When each remain ing solution in the population cannot be said to be better than any other in all OF d imensions, they are called non-dominated and are members of the local Pareto-optimal set, and are all of equal value and potential interest to the researcher. The non-dominated set of the entire feasible search space is the global Pareto-optimal set (Deb, 2001).

Figure 1. The IEEE 30-bus test system in single line diagram style, showing the

location of DG units by bus, where the V-number is the variable for the number of units of the given DG type at that bus. See also Table 1.


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3 Method The MOOEA used here is a mult i-objective optimizing genetic algorithm that self-adapts its

control parameters, implemented in Java (Oliver et al., Expected July 2014), where the term self-adaptive is used in the sense of Eiben et al. (Eiben et al., 2006) fo llowing on from the work of Bäck (Bäck, 1992) , to indicate control parameters that are encoded in the internal representation of each candidate solution along with the problem definition parameters applying to the objective functions (the main parameters), and that these control parameters are subject to change along with the main parameters due to mutation and crossover. This is d ifferent from a purely adaptive control parameter strategy as in that case the change is instigated algorithmically by some feedback at the higher level of the GA rather than the lower level of each chromo -some/solution in the population. The deterministic approach is rule-based and is not considered adaptive.

The Plexos tool is used as the source of the values of the objective functions that are evaluated and selected for, that is to say, the fitness indicators, by the MOOEA, as depicted in Figure 2.

Figure 2. The integration of Plexos with the self-adaptive multi-objective optimisation algorithm.

The problem is defined as a set of potential DG units each of which may or may not be located at a given node (bus). The DG units are defined as (i) micro-gas turbine (ii) Wind turbine and (iii) So lar photovoltaic, where a unit of value 0 means the generator is not present at the location. The scenario allows for up to 5 units of each type to be located at any of the nodes defined as variable in the network d iagram (Figure 1), which means that it is any except for the nodes 1, 2, 13, 22, 23 and 27, as these are the large fixed central OCGT power stations. Each t ransmission line between any two buses has a maximum flow capacity stated in megawatts (MW). The transmission line capacities are amended in the Plexos Xml model file which are sent to Plexos for each solution run.

The labels shown as Vn at the g iven nodes indicate the design variable number that defines the number o f units of the given generator types at that bus, and as can be seen, each of the 3 variable types can be present potentially. As there are 24 nodes at which variable DG units can be located and 3 types of generator, the design vector of each candidate solution therefore consists of 72 variables. A candidate solution is therefore a vector of n decision variables: , where n = 72. This configuration thus allows a solution to have from 0 DG units up to a theoretical 360 (being 5 units of each of 3 DG types at the 24 nodes). Table 1 below shows the allocation of DG units by type to nodes, cross-referenced to its variable number (as shown in Figure 1), with the assumption that a given generator feeds in to one associated node only.


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There are 4 objective functions defined, all of which are to be minimised simultaneously and the values for all of which come from Plexos, these being:

sumU Equation 1

|useDump| Equation 2 μspotPrice Equation 3

Equation 4 in which the values represent respectively:

i. The total number of DG units ii. The USE/DUMP energy (MWh) iii. Spot Price ($/MWh) iv. CO2 emissions (Kg)

Considering the values above, useDump, depending whether it is negative or positive, is either the un-served amount of energy due to under-production or the dump energy due to over-production, relative to demand. The spot price is the mean price achieved in the simulated market auctions over the course of the simulation in Plexos.

A hard constraint on the total number of DG units deployed, u, is applied in Equation 5, in order to investigate how the system transforms itself. Without such a constraint, which can be viewed as a limit to financial resources available as investment into DG, we would perhaps expect the system to maximize DG deployment as this provides a known benefit where cost is the only downside, and this would hide the effects that placement may have when otherwise. It is the number of DG units (and their placement) that is particu larly of interest in these studies, and having the objective function for the total DG units is important as it ensures diversity in sumU, enabling plots such as Figure 5 to be possible. The intention of this rather low constraint for this case is to encourage the optimisation to find the best locations for the ext ra DG units, rather than simply adding more units overall, to better illustrate the potential of the method.

Equation 5

The candidate solutions chosen by the MOOEA, using the results from Plexos, are thus selected

due to the effect their chosen DG units have on the electrical network due to their operating characteristics and where they feed into the network, defined in the topology as shown in Figure 1.

The MOOEA , as described at the start of section 3 above, allows each new experiment to override its default init ializer which creates an init ial population of candidate solutions by generating variables under a uniform random distribution regime within the ranges of the defined variables, in this case 0 <= u <= 5. The in itializer used instead generates solutions that meet the hard constraint, by selecting for each solution a random value between 0 and the constraint, 35, and using this as the limit for that candidate solution. Each variab le of that solution is then selected randomly, and is allocated a random value within its range, until the solution’s own limit is reached. In this way, solutions in the in itial population will vary between 0 DG units and 35 with a uniform distribution.

In subsequent generations, solutions will evolve that may break the hard constraint, due to mutation and recombination operators acting on ‘fit’ parent solutions selected for breeding, and in this case the solutions will be retained in the population but repaired. Repairing in this context means that a failing solution’s vector of DG variables is changed until it falls with in the constraint, by randomly choosing one of the variables, decrementing its DG unit count (when it has ), and then repeating the process until the total falls within the constraint.


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The MOOEA is configured to have a mixed chromosome consisting of a vector of 72 integers, for the DG genes, one per bus, with the self-adaptive control parameters encoded as real numbers. In addition, another 41 genes each contain the line maximum flow capacity (LC), in MW, of a given transmission line. In the first optimisation defined, the LC genes are fixed but one is changed to a new value, while in the following optimisation, all 41 are enabled to evolve. There is a fixed population of size 30, allowing 0 duplicate solutions in any single generation, with initial crossover and mutation probabilities of 0.9 and 0.009 (≈ 1/(72+41)) respectively. The MOOEA is allowed to run for 2,000 function evaluations (67 generations), with each generation taking around 3 hours elapsed time.

Table 1. Buses, their Variables and DG unit types t Micro-Gas Micro-Wind Solar PV Node Var Node Var Node Var n03 V01 n03 V02 n03 V03 n04 V04 n04 V05 n04 V06 n05 V07 n05 V08 n05 V09 n06 V10 n06 V11 n06 V12 n07 V13 n07 V14 n07 V15 n08 V16 n08 V17 n08 V18 n09 V19 n09 V20 n09 V21 n10 V22 n10 V23 n10 V24 n11 V25 n11 V26 n11 V27 n12 V28 n12 V29 n12 V30 n14 V31 n14 V32 n14 V33 n15 V34 n15 V35 n15 V36 n16 V37 n16 V38 n16 V39 n17 V40 n17 V41 n17 V42 n18 V43 n18 V44 n18 V45 n19 V46 n19 V47 n19 V48 n20 V49 n20 V50 n20 V51 n21 V52 n21 V53 n21 V54 n24 V55 n24 V56 n24 V57 n25 V58 n25 V59 n25 V60 n26 V61 n26 V62 n26 V63 n28 V64 n28 V65 n28 V66 n29 V67 n29 V68 n29 V69 n30 V70 n30 V71 n30 V72

4 Results Some figures below show results in the form of parallel coordinates (|| -coords), the technique

introduced and promulgated originally by Inselberg (Inselberg, 2009), and later used in the field of optimisation by (Fleming et al., 2005), (Siirtola, 2000), (Siirtola and Räihä, 2006) , and engineering design (Kipouros et al., 2008) and (Kipouros et al., 2013), in which each dimension is oriented parallel to the others, thus transforming an n-dimensional po int into a 2-dimensional polygonal line that relates the values in each dimension. This technique enables highly mult i-d imensional data to be plotted uniquely and without loss of information, and in these cases the whole design space of each solution, 72 variables, are plotted alongside their 4 objective function results. These plots were produced using the Parallax tool (Avidan and Avidan, 1999).

As a first experiment, the maximum flow capacity of just one line is altered and the results compared with a prev ious run in which all aspects are the same, including the seed for the pseudo -random nu mber generator, except fo r the line capacity. In this case, line 11 is chosen, being that between the most highly connected bus, node 6, and node 9 which has less than half the connections,


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and for which the line capacity is a low-ish 65 MW. The line’s capacity is doubled to 130 MW, a figure used by other transmission lines in the network, in the new network definit ion. The new results, for the higher line capacity, are termed R008 and the previous with original line capacity, R003.

The plot in Figure 3 shows the entire 72-variable set and the objective functions for the new result set (termed R008) with the higher line 11 capacity. This has some variables as always 0, hence these can be said to be of no relevance to further optimisation runs, allowing them to be removed in future, in order to improve optimisation performance.

The results of the objective function min imisations appear in Table 2, although sumU (the total number of DG units used) is not listed as this is always between 0 and 35, given the hard constraint. It can be seen that just changing the one line capacity from 65 MW to 130 MW improves each OF result.

Table 2. New and previous best objective function results for the first experiment

OF result R008 R003 useDump 260.00 300.73 Spotprice 21.22 21.67

CO2 1,346,914.25 1,348,057.25 The plot in Figure 3 shows that the variable v11, which contains the number of units of W ind DG

for node 6, when having the value 5, is on the many highly performing solutions, including the best solution of all. The R003 results shown in Figure 4 in a similar fashion to Figure 3, seem to indicate that the reasons for the improved performance in R008, is that the number o f DG units for node 9 are no longer so important as variables v19 (node 9, Gas) and v20 (node 9, Wind) are no longer on the optimum path in R008, while for R003 both are at maximum (5). R008 also has fewer variab les at 0, which seems to suggest the network load may be better balanced too. The scatter plot of Figure 5 shows the variation of the mean spot price against the total number of DG units (sumU), with the most converged points manually selected, and in Figure 6, the subset of those selected points in which v11 has 5 DG units, are highlighted.

Figure 3. ||-coords plot for R008 showing all 72 variables and 4 OFs, with selection of results in which

v11 has 5 units, and circled variables always 0 (v10, v38, v53, and v65).


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Figure 4. ||-coords plot for R003 showing all 72 variables and 4 OFs, with selection of results in which

v11 has 5 units.

Figure 5. A scatter plot for R008, showing sumU on x-axis against spotPrice on y-axis, with the most converged points selected by hand using the polygon tool of ParallAX.

Figure 6. The set of points selected in Figure 5 are shown here with only those that have v11=5

selected, resulting in two apparent clusters, the lower set being the best performing.


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Figure 7. ||-coords plot in which all lines’ capacities are allowed to evolve, showing the isolated solution having the best result for the useDump objective. This plot shows the 72 DG unit values and the 41 line capacity values, along with the 4 OF results.

A subsequent optimizat ion was t ried in which the maximum flow capacities of all lines were

allowed to evolve along with the DG units. In this case, the 41 line capacity (LC) genes were initialised following a Gaussian distribution using the mean and standard deviation from the first optimisation, with limits applied for a minimum of 4 MW, a maximum of 300 MW . An additional hard constraint was applied on the total flow capacity, being equal to the original p lus 20%. Figure 7 shows the isolated solution having the best result for the useDump object ive with points of interest circled and numbered. Points 1 and 2 show that line 9 (between buses 6 and 7) has both a low (47MW) and high (300 MW) value fo r the same h igh-performing solution, indicating that it is not a critical path. Its original LC was set to 130 MW, which suggests that this could be optimised down to the lower value found, although this would need to be further explored. Point 3 shows line 32 (between buses 23 and 24) has evolved down to zero (from 16 in the datum design), indicating that this line might be able to be eliminated entirely. Point 4 shows that the total of DG units was 35, as would be expected in a high-performing solution, given the constraint on the total number of units allowed. Figure 8 below shows the solutions selected by having line 20 at 300 MW, which are all high-performing and some of which are the best performing for useDump and CO2 as indicated by the brace at the bottom right of the image. Line 20 runs between buses 14 and 15.

Figure 8. ||-coords plot in which Line 20 is selected for values of 300 MW, showing that these solutions are highly performing (indicated by the brace at the bottom right).


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5 Conclusion It has been shown that this methodology, using the MOOEA with Plexos and examining the

results with a mult i-d imensional visualisation, can be used to assist in the design of network topologies from the perspective of transmission line maximum power flow capacities, by allowing the optimisation process to determine the maximum flow capacit ies along with the types and locations of DG units. It also shows that this method could be used to assist in the determination of network topology from a bus-to-bus connection perspective, through elucidation of at least best and worst lines for transmission and therefore connectivity. It should be remembered that these results relate to particular weather patterns for a reg ion in which this model power grid is imposed, and that the DG unit placement is realistic in that regard, considering micro-wind turbines and solar pv units.

6 Acknowledgements The authors again express their gratitude to colleagues and collaborators on this project, Mr Blair

Bethwaite and Dr Ariel Liebman (Monash University), Mr Leighton Brough, Dr Liam Wagner and Prof David Abramson (University of Queensland), for providing Australian weather data and the software interface to Plexos.

This work was undertaken assisted by a grant from the EPSRC (Engineering and Physical Sciences Research Council, 2014); the data and methods used are held on secure media within the Power and Propulsion Sciences group of the School of Engineering at Cranfield University (contact Professor Mark Savill).

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